Dirac tunneling magnetoresistance in a double ferromagnetic graphene barrier structure

The quantum magneto-transport properties of a double ferromagnetic graphene barrier NG/FG/NG′/FG/NG junction are investigated, where NGʹs are normal graphene layers, NG′ is a normal graphene layer of thickness d and FGʹs are ferromagnetic graphene layers of thickness L. The FG layers with exchange energy H are in contact with the gates of potential energy U. The electrical conductanceʹs (GqP and GqAP) for parallel (P) and antiparallel (AP) alignment of the polarization in the two FG layers, respectively, and the tunneling magnetoresistance (TMR) defined as (GqP−GqAP/GqP)×100% are derived. We find that at zero bias, the oscillatory behavior of the TMR for our multilayer junction has a maximal value of 50% which can be tuned by adjusting the gate voltage and exchange fields in the FGʹs. The conductance and the TMRʹs are found to exhibit periodic (oscillatory) depending on the thicknesses of the NG layer and on the value of the ferromagnetic barrier strengths χU(H) defined as U(H)L/ℏvF. It is also seen that the amplitudes of oscillation do not decrease as d, U or H increases. This is due to the relativistic nature of the mobile electrons (with the effective speed of light being the Fermi velocity vF∼106 m/s) in graphene. For junctions having d=0, we find that in the AP junction, the quantum conductance modulation due to the combination between spin up and spin down conductance does not appear. The conductance of the AP junction exhibits an oscillatory dependence on χH when d≠0.